DeepBayes：Gaussian Process

Introduction

这篇是记录高斯过程的，转载请注明。
Ref：
1.Deep Bayes Slides

The Gaussian Distribution

The marginal and conditional distributions are also Gaussians.

Functional classes

Gaussian processes

Mean values and Covariances
Mean value is constructed from a priori given deterministic function:

Covariance matrix is constructed from covariance function


所以到这时候，我们可以把高斯过程总结为：
定义在连续域伤的函数，且是每个时刻对应的高斯函数的联合分布，或者说是是一个函数集合。
Example:
squared-exponential kernel
The parameters give the overall lengthscale in dimension i


Example: Constructing new covariances from old

Using GP for nonlinear regression
Training data set
Model:

Prediction

Let us denote input test point as , and output

Consider joint training and test marginal likelihood

where and

Interpolation

Condition distribution

Smoothing

predicts what we'll see next.

Determination of covariance function parameters

Gradient based optimization

Bayesian Optimization

Acquisition functions

Summary

高斯过程建模的优点是形式闭合，但是计算量比较大。